Generalization Of Poisson Process And Applications

Poisson process originated in the mid-eighteenth century. In more than a century, many scholars in domestic or abroad have extended the Poisson models to the other research fields and studied some more complicated and useful models. These amplifications include the following respects:(1) It is considered that the arrival rate is not a constant, but a vari-able associated with the arrival time, eg. the non-homogeneous Poisson models. (2) Some scholars suppose that there are not only one skip at a arrive time, but more skips, eg. the generalized Poisson model. In this thesis we mainly discuss generalized non-homogeneous Poisson process and generalized non-homogeneous compound Poisson process.In this thesis firstly we summarized the primary notations and basic results with respect to Poisson process, non-homogeneous Poisson process and compound Poisson process and gave some new results about the additivity property and independence of increment associated with non-homogeneous Poisson process and compound Poisson process. Secondly, we extended the non-homogeneous Poisson process to a class of random point process called generalized non-homogeneous Poisson process by removing the property of single jump of non-homogeneous Poisson process and derived the generating function and some properties of generalized non-homogeneous Poisson process. At last, we defined generalized non-homogeneous compound Poisson process, tow-fold generalized non-homogeneous Poisson process and discussed their characteristics and some examples such as interregional migration, the reaching customers in malls are given.